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murdocksfamilyouoxvm
28.01.2020 •
Chemistry
Assume that each atom is a sphere, and that the surface of each atom is in contact with its nearest neighbor. determine the percentage of unit cell volume that is occupied in (a) a face- centered cubic lattice, (b) a body-centered cubic lattice, and (c) a diamond lattice.
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Ответ:
Explanation:
The percentage of unit cell volume = Volume of atoms/Volume of unit cell
Volume of sphere =![\frac{4 }{3} \pi r^2](/tpl/images/0478/4519/e60ee.png)
a) Percentage of unit cell volume occupied by atoms in face- centered cubic lattice:
let the side of each cube = a
Volume of unit cell = Volume of cube = a³
Radius of atoms =![\frac{a\sqrt{2} }{4}](/tpl/images/0478/4519/6a89b.png)
Volume of each atom =
= ![\frac{\pi *a^3\sqrt{2}}{24}](/tpl/images/0478/4519/0a4ca.png)
Number of atoms/unit cell = 4
Total volume of the atoms =![4 X \frac{\pi *a^3\sqrt{2}}{24} = \frac{\pi *a^3\sqrt{2}}{6}](/tpl/images/0478/4519/5c6fe.png)
The percentage of unit cell volume =
= 0.7405
= 0.7405 X 100% = 74.05%
b) Percentage of unit cell volume occupied by atoms in a body-centered cubic lattice
Radius of atoms =![\frac{a\sqrt{3} }{4}](/tpl/images/0478/4519/913bf.png)
Volume of each atom =
=![\frac{\pi *a^3\sqrt{3}}{16}](/tpl/images/0478/4519/07af7.png)
Number of atoms/unit cell = 2
Total volume of the atoms =![2X \frac{\pi *a^3\sqrt{3}}{16} = \frac{\pi *a^3\sqrt{3}}{8}](/tpl/images/0478/4519/f3bda.png)
The percentage of unit cell volume =
= 0.6803
= 0.6803 X 100% = 68.03%
c) Percentage of unit cell volume occupied by atoms in a diamond lattice
Radius of atoms =![\frac{a\sqrt{3} }{8}](/tpl/images/0478/4519/82520.png)
Volume of each atom =
= ![\frac{\pi *a^3\sqrt{3}}{128}](/tpl/images/0478/4519/7f450.png)
Number of atoms/unit cell = 8
Total volume of the atoms =![8X \frac{\pi *a^3\sqrt{3}}{128} = \frac{\pi *a^3\sqrt{3}}{16}](/tpl/images/0478/4519/f6485.png)
The percentage of unit cell volume =
= 0.3401
= 0.3401 X 100% = 34.01%
Ответ:
A
Explanation: